Calculate the permutation entropy

Permutation Entropy (PE) is a measure of complexity or unpredictability in time series data, and it's often used to analyze non-linear dynamics. In MATLAB, you can calculate Permutation Entropy using the `permuteEntropy` function from the `Entropies` toolbox, which comes as part of the Statistics and Machine Learning Toolbox.

Here's an overview of how to compute Permutation Entropy in MATLAB:

1. First, ensure that you have the appropriate toolbox installed. If not, install it with `installToolbox('Statistics_Toolbox')`.

2. Load your time series data into a variable, say `data`. This should be a vector or matrix representing your measurements over time.

data = [your_time_series_data];

3. Set the parameters for calculating PE, such as embedding dimension (`m`), tolerance for equal values (`r`), and length of the sequence (`lag`). These values depend on the nature of your data and desired analysis.

embedding_dim = 3; % Example value
tolerance = 0.1; % Example value
sequence_length = floor(length(data) / lag); % Choose a suitable lag

4. Now, use the `permuteEntropy` function:

pe = permuteEntropy(data, embedding_dim, tolerance, sequence_length);

5. The output `pe` will be the estimated permutation entropy of your time series.

Here's the complete code snippet:

% Ensure necessary toolbox is installed
if ~isToolboxInstalled('Statistics_Toolbox')
    error('Please install the Statistics and Machine Learning Toolbox.');
end

% Load your data
data = [your_time_series_data];

% Define parameters
embedding_dim = 3;
tolerance = 0.1;
lag = floor(length(data) / sequence_length); % Assuming no remainder

% Calculate permutation entropy
sequence_length = lag;
pe = permuteEntropy(data, embedding_dim, tolerance, sequence_length);

% Display or save the result
disp(['Permutation Entropy: ', num2str(pe)]);